1. CORRELATIONS: PART II

2. Overview  Interpreting Correlations: p-values  Challenges in Observational Research  Correlations reduced by poor psychometrics (reliability and validity) Combining measures  Individual predictors often weak Multiple regression  Correlation ≠ causation Directionality and 3 rd -variable problems Causal inference Advanced topics: Standardized betas ( β ), mediation, moderation Beyond causation: Prediction and description

3. Interpreting Correlations  Correlation coefficient  Magnitude Clinical significance, real-world significance, public health significance  p-value Probability of observing an association of a particular magnitude when no real-world relationship exists More simply: Probability the result is due to sampling error Even more simply: Probability the result is due to chance p <.05 means statistically significant, trustworthy, reliable, not due to chance

4. Statistical Significance  Depends on the observed effect (magnitude of the correlation)  Depends on the sample size

7. Challenges Encountered in Observational Research  Correlations reduced by poor psychometrics (reliability and validity)  Individual predictors often weak  Correlation ≠ causation

8. Challenges Encountered in Observational Research  Correlations reduced by poor psychometrics (reliability and validity)  Use/make better measures (next unit)  Combine measures  Individual predictors often weak  Multiple regression  Correlation ≠ causation  Methods for improving causal inferences  Prediction is fun too

9. Combining Measures  Any given item (or measure or indicator) has error  Can reduce overall error by combining items, measures, indicators  Many different ways  Complex: Many varieties of factor analysis  Elegant: Summated scale scores (add them)

16. This a different statistic than r, but the same rules apply

18. Summated Scale Scores DOESN’T KNOW FACTOR ANALYSIS STILL DOES HER JOB

19. Multiple Regression  Single predictors often weak  Human behavior is often multidetermined  Can be used to examine how well several different independent variables combine to predict a single dependent variable of interest  When to use this versus summated scale scores? r R

21. One predictor… not bad

22. Try finding some more predictors…

23. Now put them in a multiple regression…

25. Correlation ≠ Causation  Mantra of Psyc 1000  Directionality problem  3 rd -variable problem  AKA Confounding Education Level Depression Symptom Severity r = -.20

26. Correlation ≠ Causation Education Level Depression Symptom Severity r = -.20

27. Correlation ≠ Causation Education Level Depression Symptom Severity r = -.20

28. Correlation ≠ Causation Education Level Depression Symptom Severity r = -.20

29. Correlation ≠ Causation Education Level Depression Symptom Severity r = -.20 Parental SES

30. Correlation ≠ Causation Pot Smoking Ice Cream Eating r =.20

31. Causal Inference  Ability to infer (assert) causation exists on a continuum  Requirements for Causation  Internal validity: Rule out 3 rd variables (alternative explanations)  Temporal precedence  Also helpful  Stronger associations  Theoretically plausible  Corroborating experimental evidence

32. 3 rd –Variable Problem  Methodologic Control  If worried about a 3 rd variable, control for it in your sample (e.g., if worried about SES, only study doctors)  Measure 3 rd Variables  Measure potential confounders to show they are not correlated with the variables you wish to study  Statistically Control for 3 rd Variables  Easy peasy. Many statistical techniques for doing this (e.g., partial correlations, ANCOVA), but we’ll just use regression  Only works well if the potential confounder was measured well (breast milk example)

33. Statistical Control in Regression

34.  Imagine that cigarette smoking across the lifespan is correlated with physical health at age 60 (r = -.40)  If you were a cigarette company, what third variables might you blame?  Alcohol use, extraversion, income, education level, poor coping skills  Do a multiple regression and find that smoking is still associated with physical health even after controlling for those variables ( β = -.37, p <.001)

35. Temporal Precedence  Cross-sectional vs. longitudinal study  Prospective vs. retrospective study Education Level T2 Depression Symptom Severity T2 Education Level T1 Depression Symptom Severity T1

36. Temporal Precedence Education Level T2 Depression Symptom Severity T2 Education Level T1 Depression Symptom Severity T1

37. Temporal Precedence Education Level T2 Depression Symptom Severity T2 Education Level T1 Depression Symptom Severity T1 β =.03 β =.21 Education level at T1 predicts Depression at T2, while controlling for Depression at T1. More or less, Education level at T1 predicts changes in depression.

40. Mediation  Rather than examining how A causes B, focuses on a causal chain: A causing B causing C… Depression Symptom Severity T2 Education Level T1 Child Depression Symptom Severity T3

41. Moderation  Different from mediation  Also called “interaction” and “effect modification”  Means that an association varies by group  Relationship between A and B depends on C Depression Symptom Severity T2 Education Level T1 β =.21 Depression Symptom Severity T2 Education Level T1 β =.11 Males Females

42. Prediction and Description  Observational research (and correlations) are important in their own right, regardless of whether or not associations are causal  Examples  Decision-making research  Personalized medicine, MMPI, Pandora, dating  Others